Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].

The relationship between socioeconomic status, schools and bone health among adolescent females in Southern Ontario

We studied the association between socioeconomic status (SES), school attended and bone health measured by bone speed of sound (SOS) among adolescent females in Canada. 412 participants from six randomly selected schools in Southern Ontario were examined. Bone SOS was measured by quantitative ultrasound. Participant’s school and aggregate area-based census-derived (AABCD) SES were evaluated as predictors. Mean participant age was 15.7 (SD 1.0) years. Average median family income was $68,162 (SD $19,366). Median family income was non-linearly associated with bone SOS and restricted cubic splines described the relationship. Univariate regression, accounting for clustering of participants in schools, revealed a significant non-linear association between AABCD-median family income and non-dominant tibial SOS (LRT p = 0.031). Multivariable regression revealed school to have a significant impact (LRT p = 0.0001). High schools had a strong influence on the bone health of female students and this effect overrode the effect of SES.

Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen models

Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately as the presence of the free electron gas renders the total energy strongly dependent on the electron density. The embedded atom method (EAM) addresses this issue by replacing part of the total energy with an explicitly density-dependent term called the embedding function. Finnis and Sinclair proposed a model where the embedding function is taken to be proportional to the square root of the electron density. Models of this type are known as Finnis-Sinclair many body potentials. In this work we study a particular parametrization of the Finnis-Sinclair type potential, called the "Sutton-Chen" model, and a later version, called the "Quantum Sutton-Chen" model, to study the phonon spectra and the temperature variation thermodynamic properties of fcc metals. Both models give poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. We identify the power law decay of the electron density with distance assumed by the model as the main cause of this behaviour and show that an exponentially decaying form of charge density improves the results significantly. Results for Sutton-Chen and our improved version of Sutton-Chen models are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen parameter. For the sake of comparison we have also considered two other models where the distance-dependence of the charge density is an exponential multiplied by polynomials. None of these models exhibits the instability against thermal expansion (premature melting) as shown by the Sutton-Chen model. We also present results obtained via pure pair potential models, in order to identify advantages and disadvantages of methods used to obtain the parameters of these potentials.

Socio-demographic factors, smoking, symptoms, morbidities and pulmonary function and quality of life in individuals with a heavy smoking history

Objective: To determine which socio-demographic, exposure, morbidity and symptom variables are associated with health-related quality of life among former and current heavy smokers. Methods: Cross sectional data from 2537 participants were studied. All participants were at ≥2% risk of developing lung cancer within 6 years. Linear and logistic regression models utilizing a multivariable fractional polynomial selection process identified variables associated with health-related quality of life, measured by the EQ-5D. Results: Upstream and downstream associations between smoking cessation and higher health-related quality of life were evident. Significant upstream associations, such as education level and current working status and were explained by the addition of morbidities and symptoms to regression models. Having arthritis, decreased forced expiratory volume in one second, fatigue, poor appetite or dyspnea were most highly and commonly associated with decreased HRQoL. Discussion: Upstream factors such as educational attainment, employment status and smoking cessation should be targeted to prevent decreased health-related quality of life. Practitioners should focus treatment on downstream factors, especially symptoms, to improve health-related quality of life.

Soil-Transmitted Helminths, Poverty, and Malnutrition in Honduran Children Living in Remote Rural Communities

Soil-transmitted helminth (STH) infections are endemic in Honduras, but their prevalence according to the levels of poverty in the population has not been examined. The present cross-sectional study is aimed to determine the role of different levels of poverty in STH prevalence and infection intensity as well as the potential associations of STH infections with malnutrition and anemia. Research participants were children attending a medical brigade serving remote communities in Northern Honduras in June 2014. Demographic data were obtained, and poverty levels were determined using the unsatisfied basic needs method. STH infections were investigated by the Kato-Katz method; hemoglobin concentrations were determined with the HemoCue system; and stunting, thinness, and underweight were determined by anthropometry. Data were analyzed using descriptive statistics and univariate and multivariable logistic regression models. Among 130 children who participated in this study, a high prevalence (69.2%) of parasitism was found and the poorest children were significantly more infected than those living in less poor communities (79.6% vs. 61.8%; P = 0.030). Prevalence rates of Trichuris trichiura, Ascaris lumbricoides, and hookworms were 69.2%, 12.3%, and 3.85%, respectively. In total, 69% of children had anemia and 30% were stunted. Households’ earthen floor and lack of latrines were associated with infection. Greater efforts should be made to reduce STH prevalence and improve overall childhood health, in particular, among the poorest children lacking the basic necessities of life.